$x$ and $y$ are related such that $x$ is inversely proportional to the square of $y$.
If $y$ is increased by 400%, find the percentage change in $x$. Answer ...%

1. Express the inverse proportional relationship and the new value of $y$.

Since $x$ is inversely proportional to the square of $y$,
$x \propto \frac{1}{y^2}.$
If $y$ is increased by $400\%$, then
$\text{new }y = 100\%y+400\%y=500\%y=5y.$

2. Find the new value of $x$ as a fraction of the original value.

Original:
$x \propto \frac{1}{y^2}.$
New:
$x_{\text{new}} \propto \frac{1}{(5y)^2}=\frac{1}{25y^2}.$
Hence
$x_{\text{new}}=\frac{1}{25}x.$

3. Calculate the percentage change in $x$.

Percentage change in $x$:
$\frac{x_{\text{new}}-x}{x}\times 100\% = \frac{\frac{1}{25}x-x}{x}\times 100\%$
$=\left(\frac{1}{25}-1\right)\times 100\%=-\frac{24}{25}\times 100\%=-96\%.$
So $x$ decreases by $96\%$.